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Wednesday, October 12, 2016

It was Twenty Years Ago Today

The title of the famous Beatles song does not exactly apply to Devlin’s Angle. The online column
(now run on a blog platform, but unlike most blogs, still subject to an editor’s guiding hand) is in
its twentieth year, but it actually launched on January 1, 1996.

In last month’s column, I looked back at the very first post. It was a fascinating exercise to try to
put myself back in the mindset of how the world looked back then, which was about the time
when the World Wide Web was just starting to find its way onto university campuses, but had
not yet penetrated the everyday lives of most of the world’s population.

That period of intense technological and societal change – looking back, it is clear it was just
beginning, in the first half of the 1990s being more evolutionary rather than the revolutionary
that was soon to follow – and the strong sensation of change both underway and pending, is
reflected in some of the topics I chose to write about each month in that first year. Here is a list
of those first twelve posts, with hyperlinks.

Along with essays you might find in a mathematics magazine for students (February, June, July,
August, November, December), there are reflections on where mathematics and its role in the
world might be heading in the next few years.

January’s post, about the growth of computer viruses in the digital domain, was clearly in that
Brave New World vein, as I noted last month, and in February I focused on another aspect of the
rapid growth of the digital world, with a look at the ongoing debate about the future of Artificial
Intelligence. Though that field has undoubtedly made many advances in the ensuing two
decades, the core argument I summarized there seems as valid today as it did then. Digital
devices still do not “think” in anything like a human fashion (though these days it can sometimes be harder
to tell the difference).

The posts for April, May, and October looked at different aspects of the “Where is mathematics
heading?” question. Of course, I was not claiming then, nor am I suggesting now, that the core
of pure mathematics is going to change. (Though the growth of Experimental Mathematics in
the New Millennium was a new direction, one I addressed in a Devlin’s Angle post in March
2009.) Rather, I was taking a much broader view of mathematics, stepping outside the
mathematics department of colleges and universities and looking at the way mathematics is
used in the world.

The October post, in particular, turned out to be highly prophetic for my own career. Shortly
after the terrorist attack on the World Trade Center on September 11, 2001, I was contacted by
a large defense contractor, asking if I would join a large team they were putting together to bid
for a Defense Department contract to find ways to improve intelligence analysis. I accepted the
offer, and worked on that project for the next several years. (From my perspective, that project
and the work that followed did not end uniformly well, as I lamented in an AMS Noticesopinion piece in 2014.) When that project ended, I did similar work for a large contractor to the US
Navy and another project for the US Army. In all three projects, I was living in the kind of world I
portrayed in that October, 1996 column.

In fact, my professional life as a mathematician for the entire life of Devlin’s Angle has been in
that world – a way of using mathematics I started to refer to as “mathematical thinking.” In a
Devlin’s Anglepost in 2012, I tried to articulate what I mean by that term. (The term is used by
others, sometimes with different meanings, though I see strong overlaps and general
agreements among them all.) That same year, I launched the world’s first mathematical MOOC
on the newly established online course platform Coursera, with the title “Introduction to
Mathematical Thinking”, and published a book with the same title.

With the world as it is today, in particular the pervasive (though largely hidden) role played by
mathematics and mathematical ideas in almost every aspect of our lives, I would hazard a guess
that there are far more people using “mathematical thinking” than there are people doing
mathematics in the traditional sense.

If so, that would make the professions of mathematician and mathematics educator two of the
most secure careers in the world. For there is one thing in particular you need in order to
engage in (effective) mathematical thinking about a real world problem: an adequate
knowledge of, and conceptual understanding of, mathematics. In fact, that need was ever so,
but it often tended to be overlooked in the pre-digital eras, when doing mathematics meant
engaging in a lot of paper-and- pencil, symbolic computations, which meant that the bulk of
mathematics instruction focused on computation, with wide ranging knowledge and conceptual
understanding often getting short shrift.

But those days are gone. Today, we carry around in our pockets devices that give us instant
access to pretty well all of the world’s mathematical information and computational procedures
we might need to use. (Check out Wolfram Alpha.) But the thinking still has to be done where it always has: in our heads.

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The Mathematical Association of America is the world's largest community of mathematicians, students, and enthusiasts. We accelerate the understanding of our world through mathematics, because mathematics drives society and shapes our lives. Visit us at maa.org.